Aptitude Questions on Averages, Mixture and Alligations for Placements
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Q. 1 The average age of 5 students is 20 years. If one student of age 24 is replaced with a new student, the average age becomes 19 years. What is the age of the new student?
A) 16 years
B) 15 years
C) 14 years
D) 18 years
Check Solution
Ans: D) 18 years
Total age of 5 students initially = $5 \times 20 = 100$
After replacing the student aged 24, total age of 5 students = $5 \times 19 = 95$
Age of the new student = 95−(100−24)=95−76=19
Q. 2 The average of 20 numbers is zero. Out of these, at most, how many numbers can be greater than zero?
A) 19
B) 20
C) 10
D) 1
Check Solution
Ans: A) 19
For the average to be zero, the sum of positive numbers must equal the sum of negative numbers.
So, at most, 19 numbers can be positive if only 1 number is negative to balance their sum.
Q. 3 In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water should be added to make the ratio 1:2?
A) 40 liters
B) 30 liters
C) 20 liters
D) 60 liters
Check Solution
Ans: A) 40 liters
Amount of milk = $\frac{2}{3} \times 60 = 40$ liters
Amount of water = $\frac{1}{3} \times 60 = 20$ liters
Let x liters of water be added to make the ratio 1:2. Then,
$\frac{40}{20 + x} = \frac{1}{2}$
Solving, x=60−20=40
Q. 4 A person covers a certain distance at different speeds. The first half at 30 km/hr and the second half at 50 km/hr. Find the average speed.
A) 37.5 km/hr
B) 40 km/hr
C) 45 km/hr
D) 42 km/hr
Check Solution
Ans: A) 37.5 km/hr
Let the total distance be 2D.
Time taken for first half = $\frac{D}{30}$
Time taken for second half = $\frac{D}{50}$
Total time = $150\frac{D}{30} + \frac{D}{50} = \frac{5D + 3D}{150} = \frac{8D}{150}$
Average speed = $\frac{2D}{8D/150} = \frac{2 \times 150}{8} = 37.58$ km/hr
Q. 5 The average weight of 8 men is increased by 2.5 kg when one of them weighing 70 kg is replaced by a new person. What is the weight of the new person?
A) 90 kg
B) 88 kg
C) 85 kg
D) 80 kg
Check Solution
Ans: A) 90 kg
Increase in total weight = $2.5 \times 8 = 20$ kg
Weight of the new person = 70 + 20 = 90 kg
Q. 6 A jar contains a mixture of two liquids A and B in the ratio 4:3. When 10 liters of mixture is replaced with 10 liters of liquid B, the ratio of A to B becomes 2:3. What is the original quantity of mixture?
A) 35 liters
B) 40 liters
C) 42 liters
D) 45 liters
Check Solution
Ans: A) 35 liters
Let the original quantity of mixture be x liters.
Amount of A = $\frac{4}{7}x$ , Amount of B = $\frac{3}{7}x$
After replacing 10 liters,
New amount of A = $\frac{4}{7}x – \frac{4}{7} \times 10 = \frac{4x – 40}{7}$
New amount of B = $\frac{3}{7}x – \frac{3}{7} \times 10 + 10 = \frac{3x + 40}{7}$
Equating the ratio,
$\frac{\frac{4x – 40}{7}}{\frac{3x + 40}{7}} = \frac{2}{3}$
Solving for x , we get x=35
Q. 7 The average age of a group of 15 children is 10 years. If 5 more children join the group with an average age of 8 years, what is the new average age?
A) 9.5 years
B) 9 years
C) 10 years
D) 8.5 years
Check Solution
Ans: A) 9.5 years
Total age of the 15 children = $15 \times 10 = 150$
Total age of the 5 new children = $5 \times 8 = 40$
New total age = 150+40=190
New average age = $9.5\frac{190}{20} = 9.5$ years
Q. 8 Two types of rice costing Rs. 60/kg and Rs. 90/kg are mixed in the ratio 2:3. What is the price of the mixture per kg?
A) Rs. 75
B) Rs. 80
C) Rs. 78
D) Rs. 85
Check Solution
Ans: A) Rs. 75
Using the alligation rule: Price of mixture=$\frac{2 \times 90 + 3 \times 60}{2 + 3} = \frac{180 + 180}{5} = 75$
Q. 9 The average score of a class of 50 students is 72. After removing the top 5 scores, the average score becomes 70. What was the average score of the top 5 students?
A) 90
B) 82
C) 80
D) 85
Check Solution
Ans: A) 90
Total score of 50 students = $50 \times 72 = 3600$
Total score of remaining 45 students = $45 \times 70 = 3150$
Sum of top 5 scores = 3600 – 3150 = 450
Average score of top 5 students = $\frac{450}{5} = 90$
Q. 10 A mixture contains alcohol and water in the ratio 3:1. On adding 10 liters of water, the ratio becomes 2:3. What was the initial amount of alcohol in the mixture?
A) 6 liters
B) 8 liters
C) 9 liters
D) 10 liters
Check Solution
Ans: C) 9 liters
Let the initial quantity of alcohol be 3x and water x.
After adding 10 liters of water,
New ratio = $\frac{3x}{x + 10} = \frac{2}{3}$
Solving, x=9, so the initial amount of alcohol = $73 \times 9 = 27$
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